2/3 of the hits were for any site with "avatar," meaning someone's proxy.
Lots of hits for "typeface" and "movie" etc.

A few hits specifically mentioned the font, calling it Papyrus. It's verrry similar to Papyrus, but there are a number of salient differences (and there are only four characters in the word "Avatar"). Perhaps it is Papyrus with these few differences:

1. Crossbar of first A doesn't touch
2. Apexes of other A's don't touch
3. V has a calligraphic ending stroke on left leg
4. Crossbar of T is less curved than in Papyrus
5. Leg of R ascends above bowl. Bowl doesn't touch leg at the waist. Right leg of R has a different termination.

$300 Million dollar budget and all Cameron can come up with for a font is Papyrus?

:-D
It's all about priorities, I suppose.
Regardless of the font used, sure it don't seem there were a lot of work put in that logo.
But maybe they didn't use Papyrus after all (where have I seen that R already?), maybe they used a discarded Lord of the Rings typeface... or a free font.